Locating Arrangement and Method Using Boring Tool and Cable Locating Signals

ABSTRACT

An arrangement and an associated method are described in which a boring tool is moved through the ground within a given region along a path in which region a cable is buried. The boring tool and the cable transmit a boring tool locating signal and a cable locating signal, respectively. Intensities of the boring tool locating signal and the cable locating signal are measured along with a pitch orientation of the boring tool. Using the measured intensities and established pitch orientation, a positional relationship is determined to relative scale including at least the boring tool and the cable in the region. The positional relationship is displayed to scale in one view. The positional relationship may be determined and displayed including the forward locate point in scaled relation to the boring tool and the cable. Cable depth determination techniques are described including a two-point ground depth determination method.

BACKGROUND OF THE INVENTION

This application is a divisional application of copending U.S. patentapplication Ser. No. 11/437,228 filed May 19, 2006, which is adivisional application of U.S. patent application Ser. No. 10/808,918filed Mar. 24, 2004, now abandoned; which is a divisional application ofU.S. patent application Ser. No. 09/934,370 filed Aug. 22, 2001 and nowissued as U.S. Pat. No. 6,737,867 on May 18, 2004; the disclosures ofwhich are incorporated herein by reference.

The present invention relates generally to a system including a locatingarrangement for tracking a boring tool and one or more buried lines suchas, for example, pipes, cables, conduits or other conductors and, moreparticularly, to a locating arrangement configured for receiving aboring tool locating signal and at least one cable locating signal fordetermining at least one scaled positional relationship based, at leastin part, on the received locating signals.

The installation of utility lines underground is increasingly popularfor reasons of aesthetics and for practical reasons such as, forexample, protecting these lines from the effects of severe above groundweather conditions. In areas where buried lines have previously beeninstalled, however, it is undesirable to excavate an entire pathway forthe purpose of installing additional lines since such excavation manytimes results in the unintentional damage of an existing utility line.Areas which include buried fiber optic cables are particularlyproblematic for several reasons. First, a fiber optic cable is difficultto repair once it has been severed or damaged. Second, because a fiberoptic cable is capable of simultaneously carrying a vast amount ofinformation, downtime can be quite costly.

In the past, various horizontal drilling systems, including locating andmonitoring systems, have been developed which advantageously eliminatethe need for excavating the entire pathway in which a utility line is tobe installed. The attendant locating and monitoring systems serve intracking the position of the boring tool and may further serve intracking the position of one or more buried obstacles such as, forexample, utility lines. While these prior art systems are generallysuited for their intended purpose, it is submitted that a majority ofprior art approaches do not integrate boring tool and cable locatingdata. That is, the prior art generally views cable locating and boringtool tracking as entirely separate activities wherein, for example, ahandheld portable locator operates in a selected one of a cable locatingmode or a boring tool tracking mode. See, for example, a conferencepaper describing a cable locating technique based on the so-calledgradient method as reported by C. A. Young (“Measuring the depth ofburied cables”, Bell Laboratories Record, Vol. 43, No. 10, November1965).

One approach that does integrate cable and boring tool locating signaldata is described in copending U.S. patent application Ser. No.09/641,006, entitled FLUX PLANE LOCATING IN AN UNDERGROUND DRILLINGSYSTEM which is commonly assigned with the present application and whichis incorporated herein by reference. While this approach is highlyeffective and provides sweeping advantages over the state-of-the-art asof its filing date, it is submitted that still further enhancements arepossible.

Another concern with regard to the prior art resides in locatorconfigurations useful in depth determination of buried cables. Inparticular, the prior art locator includes a wand which extends belowthe locator when held by an operator. A lowermost end of the wand may beplaced on the surface of the ground during a depth measurement. Theconfiguration of the wand includes antennas at spaced apart positionswithin the extension of the wand and directed to the task of depthdetermination. It is submitted that the need for the wand provides alocator having an unwieldy, oversized configuration. See, for example, atechnical paper entitled “Alternating Magnetic Field technology forLocating Buried Utility Lines and for Providing Information for No DigTechniques”, presented in April 1985 at the NO Dig Conference in London,UK, showing a “wand” locator configured for a 2 point heightdetermination having separate, spaced apart antennas in the wand.

The present invention provides a highly advantageous enhanced locatingarrangement and associated method configured for cable and boring toollocating in a way that has heretofore been unknown and which providesstill further advantages, for example, related to cable depthdetermination, as will be described.

SUMMARY OF THE INVENTION

As will be described in more detail hereinafter, an arrangement and anassociated method are described for use in an overall system in which aboring tool is moved through the ground within a given region along apath and in which region a pre-existing cable is buried. The boring tooland the cable transmit a boring tool locating signal and a cablelocating signal, respectively, such that the boring tool locating signaland the cable locating signal are distinguishable each from the other.Intensities of the boring tool locating signal and the cable locatingsignal are measured in a predetermined way using a locator. A pitchorientation of the boring tool is established. Using the measuredintensities and established pitch orientation, a positional relationshipis determined to relative scale including at least the boring tool andthe cable in the region. In one feature, the positional relationship isdisplayed to scale in one view. In another feature, the boring toollocating signal exhibits a forward locate point at the surface of theground and the positional relationship is determined including theforward locate point in scaled relation to the boring tool and thecable.

In another aspect of the present invention, within an overall system inwhich a boring tool is moved through the ground within a given regionalong a path and in which region a cable is buried, a locatingarrangement comprises a first arrangement for transmitting a boring toollocating signal from the boring tool. A second arrangement, forming partof the locating arrangement, transmits a cable locating signal from thecable such that the boring tool locating signal and the cable locatingsignal are distinguishable each from the other. The locating arrangementfurther includes a locator for measuring intensities of the boring toollocating signal and the cable locating signal in a predetermined way andconfigured for establishing a pitch orientation of the boring tool andfor using the measured intensities and established pitch orientation todetermine a positional relationship to relative scale including at leastthe boring tool and the locator. In one feature, the locator includes adisplay arrangement configured for display of the positionalrelationship. In another feature, the boring tool locating signalexhibits a forward locate point at the surface of the ground and thepositional relationship is determined including the forward locate pointin scaled relation to the boring tool and the cable.

In still another aspect of the present invention, within a system forlocating an in-ground cable in a region using a cable locating signalwhich is transmitted from the length of the cable, a locator isdisclosed for use in sensing a first locating signal strength at a firstoperator determined distance generally in vertical alignment with anoverhead surface position, which is generally overhead of the cable, inconjunction with measuring the first operator determined distance. Thelocator is moved to a second operator determined distance from theoverhead surface position generally in vertical alignment with theoverhead surface position. A second locating signal strength is sensedat the second operator determined distance in conjunction with measuringthe second operator determined distance from the overhead surfaceposition. The depth of the cable is determined using the first andsecond signal strengths and the first and second distances.

In yet another aspect of the present invention, within a system forlocating an in-ground cable in a region using a locating signal which istransmitted from the length of the cable, a method is disclosed fordetermining the depth of the cable using a locator. Accordingly, at afirst point with reference to the surface of the ground, a generallyhorizontal locating direction is defined toward a second point. A firstintensity of the cable locating signal is measured at the first pointwith the locator oriented toward the second point along the locatingdirection. The locator is moved to the second point. A second intensityof the cable locating signal is measured at the second point. A distancebetween the first and second points is determined along the locatingdirection. Using the measured first and second intensities and thedetermined distance between the first and second points, the depth ofthe cable is determined.

In an additional aspect of the present invention, within a system forlocating an in-ground cable in a region using a locating signal which istransmitted from the length of the cable, a locator for determining thedepth of the cable is described. The locator includes a firstarrangement for sensing a signal strength of the locating signal and aprocessing arrangement cooperating with the first arrangement andconfigured for using (i) a first signal strength measured at a firstpoint with reference to the surface of the ground with the locatororiented in a generally horizontal locating direction toward a secondpoint, (ii) a second signal strength measured at the second point and(iii) a distance determined between the first and second points todetermine the depth of the cable.

In a further aspect of the present invention, within a system forlocating an in-ground cable in a region using a locating signal which istransmitted from the length of the cable, a method is described fordetermining the depth of the cable using a locator comprising the stepsof (i) at a first point with reference to the surface of the ground,defining a generally horizontal locating direction toward a secondpoint, (ii) measuring a first intensity of the cable locating signal atthe first point with the locator oriented toward the second point alongthe locating direction, (iii) moving the locator to the second point,(iv) measuring a second intensity of the cable locating signal at thesecond point, (v) determining a distance between the first and secondpoints along the locating direction, and (vi) using the measured firstand second intensities and the determined distance between the first andsecond points, determining the depth of the cable.

In another aspect of the present invention, within a region whichincludes at least one generally straight cable in the ground andextending across the region, from which cable a locating signal istransmitted, a method is disclosed comprising the steps of measuring alocal flux intensity, including three orthogonally opposed values of thelocating signal at an above ground point within the region using aportable locator, using the local flux intensity to establish anapproximate horizontal distance to the cable based on (i) a verticallyoriented component of the locating signal at the above ground pointdetermined from the local flux intensity and (ii) a horizontallyoriented component of the locating signal at the above ground pointdetermined from the local flux intensity, which horizontally orientedcomponent is generally normal to the cable in a plan view and representsa total flux intensity in a horizontal plane.

In yet another aspect of the present invention, within a system for usein a region which includes at least one generally straight cable in theground and extending across the region, from which cable a locatingsignal is transmitted, a locator is described. The locator includes afirst arrangement for measuring a local flux intensity, including threeorthogonally opposed values, of the locating signal at an above groundpoint. A processing arrangement forms part of the locator for using thelocal flux intensity to establish an approximate horizontal distance tothe cable in a plan view based on (i) a vertically oriented component ofthe locating signal at the above ground point determined from the localflux intensity and (ii) a horizontally oriented component of thelocating signal at the above ground point determined from the local fluxintensity, which horizontally oriented component is generally normal tothe cable in a plan view and represents a total flux intensity in ahorizontal plane.

In still another aspect of the present invention, within a system forlocating an in-ground cable in a region using a cable locating signalwhich is transmitted from the length of the cable, a method is disclosedfor determining the depth of the cable. A first locating signal strengthis sensed, using a locator, at a first operator determined distancegenerally in vertical alignment with a surface position which ishorizontally displaced with respect to any position directly overhead ofthe cable. The first operator determined distance from the surfaceposition is measured with the locator. The locator is moved to a secondoperator determined distance from the surface position generally invertical alignment with the surface position and sensing a secondlocating signal strength at the second operator determined distance. Thesecond operator determined distance is measured from the surfaceposition. A horizontal distance is measured from the surface position toa point directly overhead of the cable in a direction that is normal toa surface projection of the cable. The depth of the cable is determinedusing the first and second locating signal strengths, the first andsecond distances and the measured horizontal distance.

In yet another aspect of the present invention, within a system forlocating an in-ground cable in a region using a cable locating signalwhich is transmitted from the length of the cable, a locatingarrangement is described. The locating arrangement includes a firstarrangement for sensing a signal strength of the locating signal at anoperator determined distance from a surface position on the ground. Asecond arrangement forms part the locating arrangement for measuring theoperator determined distance from the surface position. A processingarrangement cooperates with the first and second arrangements and isconfigured for accepting (i) a first signal strength, measured at afirst operator determined distance generally vertically above aparticular surface position on the ground which is horizontallydisplaced with respect to any position directly overhead of the cable,and (ii) a second signal strength, measured at a second operatordetermined distance generally vertically above the particular surfaceposition, and configured for determining a depth of the cable using thefirst and second signal strength measurements and the first and secondoperator determined distances.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may be understood by reference to the followingdetailed description taken in conjunction with the drawings brieflydescribed below.

FIG. 1 is a diagrammatic perspective view of a locator produced inaccordance with the present invention shown here to illustrate variouscomponents of the locator.

FIG. 2 is a diagrammatic plan view of a region including a buried cableand a boring tool performing a drilling operation, shown here toillustrate a scaled positional relationship method of the presentinvention wherein a positional relationship between a boring tool and anin-ground cable is determined.

FIG. 2A is a diagrammatic illustration of a screen display provided, forexample, on the locator of FIG. 1, showing the scaled positionalrelationship determined in accordance with the present invention.

FIG. 3 is a diagrammatic view of a region in which an in-ground cable ispositioned, shown here illustrate a determination of a heading towardthe cable.

FIG. 4 is another diagrammatic view of the region shown in FIG. 3providing an elevational end view of the in-ground cable, shown here toillustrate further details of the determination of the cable heading.

FIG. 5 is a representation of a screen display provided, for example, onthe locator of the present invention, diagrammatically showing onepossible display of an in-ground cable in relation to the locatorwherein the cable is generally ahead of the locator.

FIG. 6 is another representation of a screen display provided, forexample, on the locator of the present invention, diagrammaticallyshowing one possible display of an in-ground cable in relation to thelocator wherein the cable is generally overhead of one point along thelength of the cable.

FIG. 7 is yet another representation of a screen display provided, forexample, on the locator of the present invention, diagrammaticallyshowing one possible display associated with a region which includes aplurality of in-ground cables in relation to the locator.

FIG. 8 is a diagrammatic elevational view of an in-ground cable, shownhere to illustrate a two-point overhead height technique for depthdetermination using first and second operator determined distances abovethe surface of the ground.

FIG. 9 is a diagrammatic plan view of an in-ground cable, shown here toillustrate a highly advantageous two-point ground method for depthdetermination performed in accordance with the present invention.

FIG. 10 is a diagrammatic end view of the cable of FIG. 9, taken along aline 12-12, showing the positional relationship between the cable andselected flux components.

FIG. 11 is a diagrammatic plan view of an in-ground cable shown here toillustrate a two-point offset height technique for depth determinationusing first and second operator determined distances above the surfaceof the ground in accordance with the present invention.

FIG. 12 is a diagrammatic end view, in elevation, of the in-ground cableof FIG. 11, taken along a line 12-12, shown here to illustrate selectedcable locating signal flux components relative to the cable and thesurface of the ground.

FIG. 13 is a diagrammatic plan view of an in-ground cable installedhaving a curved configuration in a horizontal xy coordinate system shownhere for use in facilitating a description of the influence of thecurved configuration on depth and position locating.

FIG. 14 is a plot of determined cable position versus radius of cablecurvature for the cable of FIG. 13, shown here to illustrate cableposition determination accuracy with changing curvature.

FIG. 15 is a diagrammatic plan view of a region including an in-groundcable installed at a 10 foot depth, further having an abrupt 90°directional change and still further illustrating positions at which alocator, configured for indicating a horizontal locating signal flux,indicates the position of the cable for comparison with the actual cableposition as influenced by the 90° bend.

FIG. 16 is a diagrammatic plan view of a portion of the region of FIG.15, but with the cable installed at a 1.5 foot depth, illustrating thatthe locator indicated position of the cable differs from the actualcable position near the 90° bend by a few inches but agrees well withcalculated data.

FIG. 17 is a plot of measured cable depth versus radius of cablecurvature for the curved cable configuration shown in FIG. 13,illustrating the effect of cable curvature on depth determination usingthe two-point ground depth determination method of the present inventionhaving both measurement points along the x axis on one side of the cableand within the curved configuration of the cable.

FIG. 18 is a plot of measured cable depth versus radius of cablecurvature produced consistent with the manner in which the plot of FIG.17 is produced and again using the two-point ground depth determinationmethod of the present invention, having, however, both measurementpoints at opposite points on the x axis outside the curved configurationof the cable shown here to illustrate influence on determined depth.

FIG. 19 is a plot of measured cable depth versus radius of cablecurvature produced consistent with the manner in which the plot of FIG.17 is produced and again using the two-point ground depth determinationmethod of the present invention, having, however, the measurement pointson opposite sides of the cable as well as opposite sides of the x axis,shown here to illustrate influence on determined depth for comparisonwith FIGS. 17 and 18.

FIG. 20 plots depth error, as a percentage of depth, against actualcable depth for a curved in-ground cable installed according to FIG. 13having a radius of curvature of 200, feet shown here to illustrate adepth error of less than 1% over a depth range of 2-20 feet formeasurement points on opposite sides of the cable along the x axis.

FIG. 21 plots cable depth against cable radius of curvature for a curvedin-ground cable installed according to FIG. 13 having a range of radiusof curvature from 0 to 200 feet, showing one plot determined using thetwo-point ground depth determination method of FIGS. 10 and 11 andanother plot determined using the two-point height method of FIG. 8 forcomparison of the plots.

FIG. 22 is a plan view showing an in-ground cable buried at a depth of 5feet and having a curved configuration within an xy coordinate system,shown here to illustrate two-point ground depth determination inaccordance with the present invention at spaced apart positions alongthe cable length and indicating depth error associated with each pair ofmeasurement points having the respective measurement points of each pairseparated by approximately ten feet across the buried cable in planview.

FIG. 23 is a diagrammatic plan view produced consistent with the view ofFIG. 22 but with the respective measurement points of each pairseparated by approximately two feet across the buried cable in plan viewand also indicating depth error associated with each pair of measurementpoints.

FIG. 24 is a diagrammatic plan view showing one-half of the cable ofFIGS. 22 and 23, shown here to illustrate depth determinations made atspaced apart positions along the depicted length of the cable, includinga depth error associated with each position, wherein the depth at eachposition is determined using the two point overhead method.

FIG. 25 shows depth error plotted against depth assuming a 2% fluxmeasurement error, illustrating one plot made using depth readings takenusing the two-point height method of FIG. 8 for comparison with anotherplot produced using the two-point ground depth determination method ofFIGS. 10 and 11 which employs measurement point pairs having each pointof an opposing pair on opposite sides of the cable for direct comparisonof the plots.

DETAILED DESCRIPTION OF THE INVENTION

Turning now to the drawings, wherein like items are indicated by likereference numbers throughout the various figures, attention isimmediately directed to FIG. 1 which illustrates one embodiment of aportable locator, generally indicated by the reference number 10 andconfigured in accordance with the present invention. Locator 10 includesa three-axis antenna cluster 12 measuring three orthogonally arrangedcomponents of magnetic flux in locator fixed coordinates. One usefulantenna cluster contemplated for use herein is disclosed by U.S. Pat.No. 6,005,532 entitled ORTHOGONAL ANTENNA ARRANGEMENT AND METHOD whichis commonly assigned with the present application and is incorporatedherein by reference. A tilt sensor arrangement 14 is provided formeasuring gravitational angles from which the components of flux in alevel coordinate system may be determined. Locator 10 further des agraphics display 16, a telemetry arrangement 18 having an antenna 19 anda microprocessor 20 interconnected appropriately with the variouscomponents. Other components may be added as desired such as, forexample, an azimuth sensor in the form of a tri-axial magnetometer 22 toaid in position determination relative to a selected direction such asthe drilling direction and ultrasonic transducers (not shown) formeasuring the height of the locator above the surface of the ground. Onehighly advantageous ultrasonic transducer arrangement is described, forexample, in U.S. Pat. No. 6,232,780 which is commonly assigned with thepresent application and is incorporated herein by reference.

For purposes of simplification of the present description, it isinitially assumed that any buried cable being located is straight and ispositioned at a constant depth below a level ground surface. Of course,the cable locating signal may be transmitted from a tracer wire that isassociated with the buried cable. Removal of these assumptions will beconsidered at appropriate points below.

A boring tool (not shown) suitable for use in the locating system of thepresent invention includes an axially arranged dipole antenna whichtransmits the boring tool locating signal in the form of a dipole field.It is also assumed that the boring tool is configured, as needed, forsensing and transmitting the pitch of the boring tool. Transmission ofpitch and other values may be accomplished, for example, by modulatingthe information onto the boring tool locating signal. Alternatively,such data may be transmitted using the drill string having, in oneimplementation, a conductive wire arrangement housed within the drillstring. Highly advantageous arrangements for accomplishing the latterare described in U.S. Pat. No. 6,223, 826 entitledAUTO-EXTENDING/RETRACTING ELECTRICALLY ISOLATED CONDUCTORS IN ASEGMENTED DRILL STRING and copending U.S. patent application Ser. No.09/793,056, both of which are commonly assigned with the presentapplication and are hereby incorporated by reference.

Referring to FIG. 2 in conjunction with FIG. 1, a region 100 is shownincluding a boring tool 102 which transmits a dipole locating field 104that is received by antenna cluster 12 of FIG. 1. Region 100 is shown inplan view. Boring tool 102 is at the origin of an xyz coordinate systemwhere the x and y axes define a horizontal xy plane. The x axis iscoincident with an axis of symmetry of a dipole antenna (not shown)which transmits the boring tool locating signal and which forms part ofthe boring tool, assuming the latter is at zero pitch. The positive orforward direction of the x axis (upward in the plan view of FIG. 2) mayalternatively be referred to as the drilling direction which may, inturn, be projected upward to the surface of the ground. The z axis isnot shown but extends normally outward in a positive direction from theplane of the figure. Accordingly, a forward locate point 108 is presentat or proximate to the surface of the region, as described, for example,in U.S. Pat. No. 5,337,002 entitled LOCATOR DEVICE FOR CONTINUOUSLYLOCATING A DIPOLE MAGNETIC FIELD TRANSMITTER AND ITS METHOD OF OPERATIONwhich is commonly assigned with the present application and isincorporated herein by reference. A rear locate point is also present atthe surface of the ground, but has not been illustrated for purposes ofclarity. Locator 10 is configured in a suitable manner for finding thelocate points. One highly advantageous configuration of the locatordirected, at least in part, to finding the locate points is described inabove incorporated copending U.S. application Ser. No. 09/641,006.

Continuing with a description of FIG. 2, region 100 further includes acable 110 which transmits a cable locating signal 112. As is alsodescribed in above incorporated copending U.S. application Ser. No.09/641,006, the cable locating field is two-dimensional, characterizedby a pattern of flux lines surrounding the cable which appear as lines(only one of which is shown) normal to cable 110 in the plan view ofFIG. 2. The flux lines immediately above the cable line at the surfaceof the ground accordingly are normal to its plan-view, as indicated by aflux vector 116. Having established the position of the forward locatepoint in a suitable manner, a highly advantageous procedure may beemployed for the purpose of creating a view of region 100 which has notpreviously been available, as will be described.

Referring to FIGS. 1 and 2, a drilling direction 120 is recorded forfuture reference by orienting locator 10 along the drilling directionand, thereafter, reading an azimuth angle from magnetometer 22. In thisregard, antenna cluster 12 is oriented having a receiving axis arrangedalong an axis of symmetry of the locator. Of course, the azimuth angleof the drilling direction may be recorded at any time so long as thedrilling direction has been established and prior to a need to use theazimuth angle in subsequent determinations. With the drilling directionrecorded, a locating direction 122 is then established having a headinggenerally in the direction of cable 110. Positions with respect to thelocating direction are designated with reference to an s coordinate axishaving its origin at the forward locate point and positive values in thelocating direction. The general direction of the cable may beestablished in any suitable manner. One highly advantageous technique isdescribed in above incorporated, copending U.S. application Ser. No.09/641,006, entitled FLUX PLANE LOCATING IN AN UNDERGROUND DRILLINGSYSTEM with reference to its FIGS. 10 and 11. Another highlyadvantageous technique will be described at an appropriate point below.

From the locate point, the operator moves the locator generally in thelocating direction (the positive s direction) toward the cable to aPoint 1. The preferred approach to the cable is in a direction normal tothe direction of the cable, however, deviation from this approachremains highly effective as illustrated by the example of FIG. 2. Theangle ε shown in the figure should always be chosen such that the cableinduced fluxes at points 1 and 2 are distinct. Point 1 is at anarbitrary distance from the locate point as determined by the operator.The x and y coordinates of Point 1 are x₁,y₁ while its s coordinate iss₁. The positions of points 1 and 2 with respect to the forward locatepoint and the cable are ultimately determined by the signal strengths ofthe transmitter and the cable. Signal to noise ratio for transmitter andcable must be sufficiently high to permit accurate measurements of theirrespective fluxes. As described below, among other variations, Point 1may coincide with the forward locate point wherein the distance from thelocate point is, of course, zero.

Upon establishing Point 1, readings of both the cable locating signaland the boring tool locating signal are taken at Point 1 to establishflux components of both signals. Additionally, the heading of thelocating direction is recorded with the locator oriented therealongusing a reading of magnetometer 22. The heading of the locatingdirection is denoted as an angle δ shown between the drilling directionand the locating direction in FIG. 2. Considering the orientation of thecable, an angle γ is determined and recorded which represents adirection to the cable that is normal to the cable from Point 1.Accordingly, an angle ε=90°+γ is defined in the xy plane between thedirection in which the cable extends and the locating direction. Thedetermination of γ is made based on a horizontal plane flux lineorientation exhibited by the cable locating signal, as will be furtherdescribed below.

Having completed the foregoing procedures at Point 1, the operatorproceeds to move the locator in the locating direction to a Point 2.This latter point may be at a somewhat arbitrary distance from Point 1,but the general criterion on how to select its position relative totransmitter and cable described above applies. The x and y coordinatesof Point 2 are x₂,y₂ while its s coordinate is s₂. The distance betweenPoints 1 and 2 is indicated as Δs. It should be noted that the zcoordinate, z₃, of these points is equal to the depth of the boringtool, since a level ground surface is assumed.

Coordinates of Points 1 and 2, in the xyz and s coordinate systems, maybe determined using the recorded flux intensities established for theboring tool locating signal at Points 1 and 2 based upon the dipoleequations in conjunction with measured pitch of the boring tool,horizontal distance, x_(LP), between the boring tool and the forwardlocate point, angle δ, and a determined depth D_(T) of the boring tooldetermined, for example, using the boring tool locating signal based onthe dipole equations in a known manner.

With continuing reference to FIGS. 1 and 2, the s coordinates of Points1 and 2 may be determined using:

s ₁ ²=(x ₁ −x _(LP))² +y ₁ ²  (1)

s ₂ ²=(x ₂ −x _(LP))² +y ₂ ²  (2)

under the condition that s=0 at the forward locate point. The value ofΔs is given by:

Δs=s ₂ −s ₁  (3)

The coordinates s₃ and x₃,y₃ (z₃=D_(T), the depth of the boring tool)may be determined, in view of equations 1-3, by solving the equations:

$\begin{matrix}{s_{3} = {s_{1} + {\frac{D_{c}}{\cos \; \gamma}\frac{b_{w\; 1}}{b_{h\; 1}}}}} & (4) \\{x_{3} = {x_{LP} + {s_{3}\cos \; \delta}}} & (5) \\{y_{3} = {s_{3}\sin \; \delta}} & (6)\end{matrix}$

where b_(w) ₁ and b_(h) ₁ are components of the cable locating signaldetermined at the first point with b_(w) ₁ being an intensity componentnormal to the xy plane and b_(h) ₁ a total intensity component of thecable locating signal in the plane of the ground, s₁ represents the scoordinate of the first point, s₂ represents the s coordinate of thesecond point, x₁,y₁ represents the xy coordinates of the first point,x₂,y₂ represents the xy coordinates of the second point, x_(LP)represents the x coordinate of the forward locate point and D_(c) is thedepth of the cable. The latter may be determined in any suitable manner;however, at least one highly advantageous technique is described below.

A number of possible approaches may be used in order for the locator todistinguish between the signal from the boring tool transmitter and oneor more buried cable lines. For example, a different frequency may beused for each item being located or tracked. The same tri-axialreceiving antenna 12 (see FIG. 1) may be used to receive all theemployed frequencies. A digital signal processing receiver is used toextract the signal amplitudes for each antenna and frequency.Alternatively, different sets of receiving devices may be used. In anycase, a microprocessor is configured for processing the data fordisplay. In the case of AC power cables, with separated neutrals, thesignal naturally emanating from the AC cable may be used as the cablelocating signal. If more than one cable is present, however, a differentfrequency for each cable may be employed. The location data for eachcable may be presented alone or in combination with the location datafor other cables.

One alternative to multiple frequency use is the use of time multiplexedsignals that are synchronized at the locator. Such multiplexing may beused for the cable lines in the ground or may include the boring tooltransmitter as well. Combinations of multiple frequencies and timemultiplexing are also contemplated.

Turning to FIG. 2A, having established the location of Point 3 directlyabove the cable, it is important to note that all information necessaryto producing a scaled view of region 100 has been determined.Accordingly, FIG. 2A illustrates one possible appearance of display 16on locator 10 showing a scaled view of region 100 including the relativepositions of boring tool 102, forward locate point 108 and cable 110.The drilling path is indicated using a dashed line 120 which is seen tointersect cable 110 at a potential collision point 122 that is deadahead of the boring tool along the drilling path. This feature, in andby itself, is considered to be highly advantageous. That is, theillustration on display 16 provides the operator with an invaluableillustration of the distance to the potential collision point with cable110. Since the operator has also determined the location of the forwardlocate point as well as the position of the boring tool, the scaleddisplay serves to establish and illustrate the relative distance to thepotential collision point in terms of horizontal distance X_(LP) (seeFIG. 2) between the boring tool and the forward locate point. The scaleddisplay and method of generating essentially establishes two positionalrelationships which are scaled relative to one another: a firstpositional relationship between the boring tool and the locator and asecond positional relationship between the cable and the locator. Boringtool locating signal data and cable locating signal data are usedcooperatively in order to derive the described advantages.

It should be appreciated that displays other than the plan view of FIG.2 a may be produced. For example, an elevational view (not shown) may begenerated which illustrates the current depth of the boring toolrelative to the depth of the cable which lies ahead. Accordingly, theoperator may cause the boring tool to maintain its current depth or tobe steered either upward or downward in order to avoid a collision withthe cable, assuming that the operator's choice is to continue drillingstraight ahead in plan view.

With the foregoing procedure in mind, it should be appreciated thatvarious steps forming portions of the procedure may be modified insuitable ways. For example, it is not a requirement for Point 1 andPoint 2 to be on the near side of cable 110 with respect to the boringtool. These points may be on opposite sides of cable 110. In anothermodification, mentioned above, Point 1 may coincide with the forwardlocate point. In this instance, Point 2 may be between Point 1 and thecable or, alternatively, on the opposite side of the cable. As anothermodification, Points 1 and 2 may both be on the opposite side of thecable with respect to the boring tool and forward locate point. Theprocedure is also applicable in situations where the forward locatepoint and boring tool are on opposite sides of the cable. In view ofthese modifications, it should be appreciated that the locatingprocedure of the present invention described above remains effectiveessentially irrespective of the initial layout in the drilling region.

Referring to FIG. 2, if the foregoing scaled view locating procedure isperformed using a locator that does not incorporate a magnetometer, theprocedure may be modified by selecting the locating direction as one ofthe drilling direction (δ=0°) and a direction that is normal to thedrilling direction (δ=90°). The preferred direction should be selectedas the one of these two choices which most closely approaches normal tothe cable. That is, angle ε is closest to 90°.

Turning to FIGS. 3 and 4, attention is now directed to a highlyadvantageous procedure for determining a heading toward cable 110 inregion 100 using the locator of the present invention. This procedure isappropriate for performing a preliminary survey of a drilling region orfor use when a boring tool locating signal is not available for somereason. As an example of the latter, the locator may be out of range ofthe boring tool for purposes of boring tool locating signal reception.Moreover, the heading toward the cable may be determined in this mannerwithin the context of any locating procedure, as needed. Cable 110 isagain assumed to be generally straight at a constant distance beneaththe surface of the ground. As illustrated in FIG. 3, the locator is at apoint A and flux components b_(u) and b_(v) of cable locating signal 112are measured in a horizontal plane proximate to the surface of theground. Component b_(u) is parallel to an orientation direction 130along which the axis of symmetry of the locator is assumed to beoriented while component b_(v) is normal to orientation direction 130.FIG. 4 is an illustration of an end view of cable 110 showing a circularflux line 132 of the cable locating signal. Comparing FIGS. 3 and 4shows that flux components b_(u) and b_(v) may be added as vectors toproduce a total flux magnitude in the horizontal plane which isindicated as b_(h). That is, a total horizontal plane flux magnitude isdetermined as:

$\begin{matrix}{b_{h} = \sqrt{b_{u}^{2} + b_{v}^{2}}} & (7)\end{matrix}$

An angle γ, shown in FIG. 3, formed between the locator's orientation orlocating direction and normal to the cable, is defined as:

$\begin{matrix}{{\tan \; \gamma} = \frac{b_{v}}{b_{u}}} & (8)\end{matrix}$

It is noted that this definition is consistent with angle γ of FIG. 2such that γ may be determined using equation (8).

Referring to FIG. 4, a radial distance r extends from the cable to pointA. The total flux intensity of the cable locating signal is indicated asb_(t) and is given by:

b _(t)=√{square root over (b _(h) ² +b _(w) ²)}  (9)

where b_(w) is the vertically oriented component of the locating signalas determined using the locator. An angle α is defined, as shown atpoint A, in a direction that is normal to radial distance r measuredbetween the radial distance and a horizontal plane 134 which coincideswith the ground surface in the present example. Hence,

$\begin{matrix}{{\tan \; \alpha} = {\frac{b_{w}}{b_{h}} = {\frac{b_{w}}{b_{u}}\frac{1}{\sqrt{1 + \left( \frac{b_{v}}{b_{u}} \right)^{2}}}}}} & (10)\end{matrix}$

Angle γ gives the normal direction to the cable from point A while theangle α is used in estimating the horizontal distance to the cable. Withregard to α it is noted that α goes to plus and minus 90° at an infinitedistance in opposing directions from the cable. Thus, the sign of αdetermines whether the cable is ahead of or behind the locator. At apoint directly overhead of the cable α is equal to 0°.

Referring to FIG. 5, by knowing the direction to the cable and having abasis for distance measurement, screen 16 of locator 10 is used todisplay the location of the cable relative to the locator. A set ofcrosshairs 140 is shown at the intersection of which is the locatorposition. The orientation axis of the locator coincides with a verticalcrosshair axis 140 a. Angle γ need not be shown in the actual displaybut is shown here in order to assist the reader's understanding of theillustration. Approaching the cable at some angle γ will show the cablein the upper two quadrants defined by the crosshairs.

FIG. 6 illustrates display 16 with the locator positioned immediatelyabove the cable. Accordingly, virtual cable 110 is shown crossing thecenter of the display, intersecting the crosshairs at an angle based onγ. The angular orientation of the cable, of course, depends on thedirection in which the locator is oriented. The task of locating acable, per this procedure, simply requires an operator to move thelocator in a way which moves the line representing the cable to thecenter of the display. This can be accomplished by approaching the cablealong any convenient path, which need not be straight.

Turning to FIG. 7, a plurality of cables may be displayed simultaneouslyso long as the respective cable locating signals are distinguishable,each from the others in some suitable manner. For example, each cablelocating signal may be emanated at a different frequency. FIG. 7illustrates the appearance of display 16 showing three cables 110 a-csimultaneously displayed using a different display appearance for eachcable.

Attention is now directed to a number of highly advantageous techniquesfor use in determining cable depth. It is noted that all of the depthdetermination techniques described herein are compatible for use withlocator 10, which includes tri-axial antenna arrangement 12 (see FIG. 1)configured for measuring flux components at a single point. Moreover, asdescribed, locator 10 includes a sensing arrangement for measuring thedistance from the locator to the surface of the ground which providesfor appreciable convenience in the execution of these depthdetermination techniques as well as in the execution of other locatingtechniques such as those described above.

Referring to FIG. 8, a first depth determination technique is referredto as a two-point overhead height method and is generally indicated bythe reference number 150. An elevational view, taken in cross-section,shows region 100 including cable 110 beneath surface of the ground 134,which is considered as a horizontally extending plane. The total flux ofthe cable locating signal and distance to the ground are measured at 2different heights, h₁ and h₂, directly overhead of the cable,representing two distances from the cable. At each height, the totalflux intensity b₁ and b₂, respectively, is inversely proportional to thedistance between receiver and cable. Each distance includes height aboveground h₁ or h₂ plus the cable depth D_(c). The latter may be determinedfrom:

$\begin{matrix}{D_{c} = \frac{{h_{2}b_{2}} - {h_{1}b_{1}}}{b_{1} - b_{2}}} & (11)\end{matrix}$

It is important to understand that h₁ and h₂ are operator determineddistances which are readily measured by locator 10 using its ultrasonicdistance measuring configuration. No constraints are placed on theoperator with regard to selecting these heights, thereby permittingflexibility. Moreover, a compact locator is provided, having eliminatedany need to provide spaced apart antenna arrangements directed to thepurpose of depth determination.

Referring to FIG. 9 with supplemental reference to FIG. 3, a seconddepth determination technique is referred to as a two-point groundmethod and is generally indicated by the reference number 160. A planview is shown which illustrates cable 110 in region 100. A firstmeasurement of cable locating signal flux is conducted at a position P1adjacent to the cable with the locator pointing to a position P2. Thiswill provide angle γ as described with regard to FIG. 3, above, using

$\begin{matrix}{{\tan \; \gamma} = \frac{b_{v_{1}}}{b_{u_{1}}}} & (12)\end{matrix}$

b_(v) ₁ and b_(u) ₁ represent horizontal plane components of the cablelocating signal at P1 which add vectorially to produce b_(h) ₁ . Thelatter is determined by:

b _(h) ₁ =√{square root over (b _(u) ₁ ² +b _(v) ₁ ²)}  (13)

Subsequently, locator 10 is moved to position P2. A distance, Δs, ismeasured between P1 and P2. Where a boring tool locating signal isunavailable for purposes of position determination, any suitable lengthmeasuring technique may be used, even including that of approximating 3feet by the step of an average person. At position P2, the components ofhorizontal flux are recorded as b_(v) ₂ and b_(u) ₂ and used tocalculate total horizontal flux from

b _(h) ₂ =√{square root over (b _(u) ₂ ² +b _(v) ₂ ²)}  (14)

Since, at point P2, the fluxes are not used to determine an angle, thereceiver may be oriented in any convenient horizontal direction as thefluxes are measured.

FIG. 10 is an end view of region 100 showing cable 110 and thepositional arrangement which obtains between the cable and the fluxcomponents at the two points. Triangulation in FIG. 10, in view of FIG.9, provides the following formula for cable depth in which all variableshave been defined and determined as described above:

$\begin{matrix}{D_{c} = {\frac{\left( {\Delta \; s} \right)\cos \; \gamma}{\frac{b_{w_{1}}}{b_{h_{1}}} - \frac{b_{w_{2}}}{b_{h_{2}}}}.}} & (15)\end{matrix}$

The two-point ground method for depth determination may be performed inseveral different ways with regard to the placement of points P1 and P2with respect to cable 110. For example, the points may be arranged toone side of the cable in plan view. As another example, the points maybe arranged on opposite sides of the cable. The latter is considered tobe highly advantageous for particular reasons that will be described atan appropriate point in the remaining discussions.

With reference to FIGS. 11 and 12, a third cable depth determinationtechnique is illustrated, generally referred to by the reference number180, and may be referred to as the two-point offset height method of thepresent invention. FIG. 11 is a plan view of region 100 showing cable110 and a point C on the surface of the ground laterally displaced withrespect to any point which is directly overhead of the cable. FIG. 12 isan elevational view in cross-section showing cable 110 and point Claterally displaced from directly overhead of the cable. Locator 10 ofFIG. 1 is used to conduct measurements in general vertical alignmentwith point C at two different heights above the ground, h₁ and h₂. Ateach height, three flux components are measured as well as distance tothe ground. It is noted that s is the distance normal to the cablemeasured along a level ground surface and may be determined in anysuitable manner including, but not limited to using a boring toollocating signal or actual measurement which may, for example, be pacedoff based on the operator's stride. The total fluxes at heights h₁ andh₂ follow from

b ₁ ² =b _(u) ₁ ² +b _(v) ₁ ² +b _(w) ₁ ²  (16)

b ₂ ² =b _(u) ₂ ² +b _(v) ₂ ² b _(w) ₂ ²  (17)

where b₁ and b₂ represent the total flux at h₁ and h₂. Individual fluxcomponents are not shown for purposes of clarity, but may readily beunderstood by referring to FIG. 3. Accordingly, b_(u) is a horizontalflux component along the axis of symmetry of the locator including theappropriate number subscript, b_(v) is a horizontal flux componentnormal to the axis of symmetry of the locator including the appropriatenumber subscript and b_(w) is a vertical flux component normal to theassumed horizontal ground plane including the appropriate numbersubscript for each height. It should be mentioned that these variousflux components may be determined with locator 10 in an arbitraryorientation since the locator may determine the desired horizontal planeand vertical flux components from actual measurements with reference,for example, tilt sensor arrangement 14.

As seen in FIG. 12, slant distances for each height, r₁ and r₂ aredefined as:

r ₁ ² =s ²+(D _(c) +h ₁)²  (18)

r ₂ ² =s ²+(D _(c) +h ₂)²  (19)

Since the total flux is inversely proportional to slant distance:

$\begin{matrix}{\frac{b_{1}}{b_{2}} = \frac{r_{2}}{r_{1}}} & (20)\end{matrix}$

Based on the foregoing, the following quadratic equation for cable depthD_(c) is obtained:

$\begin{matrix}{\left( \frac{b_{1}}{b_{2}} \right)^{2} = \frac{s^{2} + \left( {D_{c} + h_{2}} \right)^{2}}{s^{2} + \left( {D_{c} + h_{1}} \right)^{2}}} & (21)\end{matrix}$

Equation (24) can be solved using any of several standard methodssatisfying the requirement D_(c)>0.

The foregoing examples have assumed a level ground surface and astraight cable at a constant depth in the ground. The cable position, inplan view, is identified as that location on or somewhat above thesurface of the ground at which the flux of the cable locating signal ishorizontally oriented. Removal of these assumptions will be consideredimmediately hereinafter.

Referring to FIG. 13, where the ground surface and/or cable depth changesomewhat gradually, cable position determination is not likely toexperience significant inaccuracy. A more difficult situation arises,however, if the cable is curved even though a constant depth ismaintained. Cable curvature of this kind is addressed herein using thecable geometry shown in a plan view in FIG. 13 wherein a cable 200 inregion 100 includes a curved portion (quarter circle) 202, at each endof which an infinitely long straight cable segment 204 is attached. Thecurved cable defines a horizontal xy plane. The magnetic fieldsurrounding this cable is determined from a solution of the law ofBiot-Savart in which the curved part of the cable is represented byforty segments (not shown) of equal length. The solution determines allpositions in a horizontal plane at or slightly above the ground surfaceat which the locating flux is horizontally oriented.

Attention is now directed to FIG. 14 in which the x coordinate of cableposition is plotted along the vertical axis against the radius of cablecurvature along the horizontal axis varying from 50 feet to 500 feet fora cable depth of 5 feet. The y coordinate is set to the value zero. Asseen in FIG. 13, the actual x coordinate of the cable for y=0 is x=0.The worst case value of the x position coordinate occurs at the tightestradius of curvature, 50 feet, exhibiting an error of approximately −0.55feet in the x coordinate position. As the radius of curvature increases,the value determined for the x coordinate more closely approaches x=0.1feet. In all cases, the x coordinate is shifted at least slightly in thenegative direction away from the actual curved cable (x<0). Accordingly,especially for radii of cable curvature larger than 100 feet, the errorappears to be essentially negligible.

Referring to FIG. 15, larger deviations between actual and observedcable position may be expected if the cable suddenly changes directioneven without changing depth. FIG. 15 shows region 100 having a cable210, indicated as a dashed line arranged along the x and y axes with asharp 90 degree bend at the origin of the coordinate system. The cableis installed at a constant 10 foot depth. The magnetic field surroundingthe cable was again derived from the law of Biot-Savart. Consistent withthe previous example, the cable position is determined by finding allpoints above or at the ground surface where the flux of the cablelocating signal is horizontal. The calculated position of the cable isindicated as a solid line 212. FIG. 15 shows the indicated cableposition to deviate in the worst case from the actual position by up to2.5 feet at points 214 and 216. It is noted that the location of thecable at the 90 degree bend itself is determined accurately.

FIG. 16 is a plan view similar to that of FIG. 15 which illustratesresults of the calculations as performed with regard to FIG. 15, but fora 1.5 foot cable depth. The calculated position of the cable is againindicated by the reference number 212. As distance increases from thebend, the indicated cable position approaches the actual cable location.In the present example, the small value of cable depth was chosen tofacilitate empirical measurements using an actual walk-over locatormanufactured by Digital Control Incorporated. Each cable positiondetermined using the locator is indicated by an asterisk (*). As isapparent from the figure, measured data and results from themathematical model agree remarkably well thereby serving to confirm thevalidity of the simulation.

Having described three different depth measurement techniques in theforegoing discussions, attention is now directed to consideration of theaccuracy of these methods with the introduction of cable curvature.Initially, the two-point ground depth determination method of thepresent invention will be considered. To that end, the effect of cablecurvature on the use of the two-point ground method is determined basedon equation (15). For the curved cable configuration shown in FIG. 13with the cable at a depth of 5 feet, depth is calculated using fluxesobtained from the described mathematical simulation of the magneticfield.

Turning to FIGS. 13 and 17, the cable depth is determined using pointsx1 and x2, indicated on the x axis of FIG. 13 where x1 is at 5 feet andx2 is at 15 feet in the positive direction, such that both of the pointsare to one side of cable 202. FIG. 17 illustrates determined cabledepth, indicated as a plot 220, plotted against a wide range of radii ofcable curvatures from 0-1000 feet along the horizontal axis. It is notedthat a negative peak 22 in the plot represents an error of more than 20%in the determined depth for a curvature having a radius of approximately40 feet. For larger radii of curvature, the depth more closelyapproaches 5 feet with error becoming essentially negligible. Measureddepth is less than the actual depth in all cases.

Referring to FIGS. 13 and 18, cable depth measurements are taken at x3,which is at −5 feet with respect to the origin, and at x4, which is at−15 feet with respect to the origin. Thus, the measurement positions areat mirror image positions on the x axis with regard to the previousexample. Cable depth is again plotted as a plot 230 against the range ofradius of curvature. Comparison of plot 220 of FIG. 17 with plot 230shows some difference which is attributable to the measurement pointsbeing outside the curvature of the cable.

Considering FIGS. 13 and 19, cable depth measurements are taken at x1and x3 at plus and minus five foot distances, respectively, from theorigin on opposite sides of cable 202. Cable depth is here plotted as aplot 240 against the range of radius of curvature from 0 to 100 feet.Measured depth is again lower than actual depth. Remarkably, the worstcase error in the depth determination is substantially reduced to avalue of approximately 5%. Hence, depth measurement using measurementpoints on opposing sides of the cable is considered to be highlyadvantageous with regard to error introduced as a result of cablecurvature. It should also be mentioned that the depth measurement errorapproaches zero (see FIGS. 17-19) as the radius of curvature approachesinfinity, irrespective of the arrangement of the measurement points ononly one or opposing sides of the cable. The reason for thischaracteristic can be found in cable depth equation 15, which is exactfor straight and level cables and applies to an approximation for curvedcables.

FIG. 20 shows a plot 250 of depth error along the vertical axis as apercentage of actual cable depth on the vertical axis against actualcable depth on the horizontal axis in the range of 0-200 feet, asdetermined using the highly advantageous two-point ground depthdetermination method of the present invention employing the opposingside measurement points at x1 and x3. A cable bend radius of 200 feet isused. As is apparent from the plot, depth error resulting from cablecurvature is readily maintained below 1% across a typical range of depthvalues.

Turning to FIG. 21, the two-point overhead method described with regardto FIG. 8 will now be considered in terms of depth measurement accuracyusing equation (11) where the required fluxes are also obtained from thepreviously described model using the law of Biot-Savart for a curvedcable. FIG. 21 includes a vertical axis showing cable depth and ahorizontal axis showing radius of cable curvature. The actual cabledepth is set to 5 feet. A plot 260 shows determined depth variationproduced from cable curvature using results from the two-point groundmethod with measurements taken at x=+4.5 feet and −5.5 feet on the xaxis of FIG. 13. A plot 270 is shown for determinations made using thetwo-point height of FIG. 8 wherein the height distance between the twopoints has a typical value of 18 inches. As seen in FIG. 21, the mostsignificant difference between the two plots is seen in a particularrange of somewhat smaller cable bend radii from approximately 0-40 feet,however, both methods provide generally accurate depth readings.

FIG. 22 illustrates a locating scenario in region 100 wherein a cable300 is installed having a bend. Such situations are typical, for examplearound street corners or to avoid in-ground objects. Accordingly, it maybe appropriate to make depth determinations at spaced apart positionsalong the length of the cable with respect to the bend. A series of foursuch measurements is shown to one side of the bend with measurementstaken using the two-point ground depth determination method of thepresent invention. Measurements are made at points across the cable withrespect to one another and separated by approximately ten feet. Eachpair of points used in a measurement are interconnected by a linesegment. Depth error is also indicated adjacent to each pair ofmeasurement points. The cable bend radius is 20 feet while the cabledepth is 5 feet.

FIG. 23 illustrates the locating scenario of FIG. 22 again showing cable300. In this example, the pairs of points for use in the two-pointground depth determination method are arranged more closely together,for example, separated by approximately two feet across the cable. Inthis case, a depth error of less than 5% was exhibited for allmeasurements. While the points of each pair used in this example may beshown as being generally equidistant from the cable, it is to beunderstood that this is not a requirement.

FIG. 24 illustrates the use of the two-point overhead height method forthe locating scenario of FIG. 22 showing only one-half of cable 300 atan expanded vertical scale. As shown in FIG. 24, depth was determined atfour spaced apart positions along the cable length using heights of 2inches and 20 inches above the surface of the ground at each point. Anerror of less than 7% was seen across all of the positions, withincreasing error as the bend was approached.

Having considered depth determination errors based on cable curvature,the effects of flux measurement error will now be addressed with regardto cable depth determination. The effects of this error on the two-pointground method of the present invention will initially be considered. Inthis regard, it is assumed that measurements are conducted in adirection normal to the plan view of the cable and the distance betweenthe measurements points 1 and 2 of each pair of points is known exactly.Application of a standard error analysis technique to the depthmeasurement equation (17) yields the following closed form solution forthe depth error E_(D) as a function of flux measurement error E_(b):

$\begin{matrix}{\frac{E_{D}}{D_{c}} = {\sqrt{2}\frac{E_{b}}{b}\sqrt{\frac{x_{1}^{2} + x_{2}^{2}}{\left( {\Delta \; s} \right)^{2}}}}} & (22)\end{matrix}$

Here the relative flux measurement errors E_(b)/b of all flux componentsb are assumed to have the same value, typically about 2%. x₁ and x₂ aremeasurement positions spaced from overhead of the cable in plan viewseparated by distance Δs. It should be appreciated that the depth erroris a minimum if, for a fixed distance |Δs|=|x₁−x₂|, the x-coordinatesx₁,x₂ have the smallest possible values. However, this requires thatpoints 1 and 2 are on opposite sides of the cable.

The effect of flux error on results obtained using the two-pointoverhead height method is now described. Again, this method relies onequation (11) to calculate depth from the measured horizontal fluxes anddistances to the ground. Without loss of generality, it is assumed thatthe first measurement is taken on the ground surface itself (h₁=0).Furthermore, the location of the second point h₂ is assumed as knownexactly. With these assumptions, a closed form solution for the deptherror is found as a function of flux error:

$\begin{matrix}{\frac{E_{D}}{D_{c}} = {\sqrt{2}\frac{E_{b}}{b}\left( {1 + \frac{D_{c}}{h_{2}}} \right)}} & (23)\end{matrix}$

It should be noted that in this case depth error, E_(D), changesquadratically with depth, resulting in very large depth errors forpractical values of h₂.

Referring to FIG. 25, depth error based on flux measurement error isshown plotted against depth for the two-point height method, indicatedas a plot 400 and for the two-point ground depth determination method,indicated as a plot 410. When directly compared, the two-point groundmethod of the present invention exhibits far less flux measurement errorinfluence than the two-point height method with increasing depth. Forexample, at a depth of 10 feet and using h₂=18 inches the depth error isexpected to exceed two feet for the two point height method: an error ofover 40%. In contrast, the depth error for the two-point ground depthdetermination is an order of magnitude smaller. This is considered to bea remarkable and highly advantageous difference in and by itself.

It should be noted that the present invention is not limited to theembodiments and methods described herein since one having ordinary skillin the art may readily implement a wide range of modifications in viewof the overall teachings herein. Therefore, the present examples are tobe considered as illustrative and not restrictive, and the invention isnot to be limited to the details given herein, but may be modifiedwithin the scope of the appended claims.

1-73. (canceled)
 74. In a region which includes at least one generallystraight cable in the ground and extending across said region, fromwhich cable a locating signal is transmitted, a method comprising thesteps of: measuring a local flux intensity, including three orthogonallyopposed values, of the locating signal at an above ground point withinsaid region using a portable locator; and using the local flux intensityto establish an approximate horizontal distance to the cable based on avertically oriented component of the locating signal at the above groundpoint determined from the local flux intensity and a horizontallyoriented component of the locating signal at the above ground pointdetermined from the local flux intensity, which horizontally orientedcomponent is generally normal to the cable in a plan view and representsa total flux intensity in a horizontal plane.
 75. The method of claim 74wherein the vertically oriented component of the locating signal isdenoted as b_(w) and the horizontally oriented component of the locatingsignal is denoted as b_(h) and wherein the approximate horizontaldistance is estimated based on an angle α determined by the expression:${\tan \; \alpha} = {\frac{b_{w}}{b_{h}}.}$
 76. The method of claim 75wherein the locator includes an axis of symmetry and wherein b_(h) isgiven by$b_{h} = {b_{u}\sqrt{1 + \left( \frac{b_{v}}{b_{u}} \right)^{2}}}$where b_(u) is measured along the axis of symmetry of the locator withthe axis of symmetry horizontally oriented and b_(v) is measuredhorizontally normal thereto.
 77. The method of claim 75 wherein tan αincludes a sign and said method includes the step of using the sign of αto establish whether the cable is ahead of or behind the locator. 78.The method of claim 75 further comprising the step of determining anangle γ between a direction that is normal to the cable in a plan viewand the locating direction given by the expression${\tan \; \gamma} = \frac{b_{v}}{b_{u}}$ such that γ establishes arelative direction of the cable from the locator at the above groundpoint with the locator oriented in the locating direction.
 79. Themethod of claim 78 wherein said locator includes a display and whereinsaid method further comprises the step of displaying a positionalrelationship between the locator, oriented along said locating directionat the above ground point, and the cable based on γ and α.
 80. In asystem for use in a region which includes at least one generallystraight cable in the ground and extending across said region, fromwhich cable a locating signal is transmitted, a locator comprising: afirst arrangement for measuring a local flux intensity, including threeorthogonally opposed values, of the locating signal at an above groundpoint; a processing arrangement for using the local flux intensity toestablish an approximate horizontal distance to the cable in a plan viewbased on a vertically oriented component of the locating signal at theabove ground point determined from the local flux intensity and ahorizontally oriented component of the locating signal at the aboveground point determined from the local flux intensity, whichhorizontally oriented component is generally normal to the cable in aplan view and represents a total flux intensity in a horizontal plane.81. The locator of claim 80 wherein the vertically oriented component ofthe locating signal is denoted as b_(w) and the horizontally orientedcomponent of the locating signal is denoted as b_(h) and wherein theprocessing arrangement is configured for estimating the approximatehorizontal distance based on an angle α determined by the expression:${\tan \; \alpha} = {\frac{b_{w}}{b_{h}}.}$
 82. The locator of claim81 including an axis of symmetry and wherein the processing arrangementis configured for determining b_(h) using the expression$b_{h} = {b_{u}\sqrt{1 + \left( \frac{b_{v}}{b_{u}} \right)^{2}}}$where b_(u) is measured along the axis of symmetry of the locator withthe axis of symmetry horizontally oriented and b_(v) is measuredhorizontally normal thereto.
 83. The locator of claim 81 wherein theprocessing arrangement is configured for determining a sign of tan α andfor using the sign of α to establish whether the cable is ahead of orbehind the locator.
 84. The locator of claim 81 wherein the processingarrangement is configured for determining an angle γ between a directionthat is normal to the cable in a plan view and the locating directiongiven by the expression ${\tan \; \gamma} = \frac{b_{v}}{b_{u}}$ suchthat γ establishes a relative direction of the cable from the locator atthe above ground point with the locator oriented in the locatingdirection.
 85. The locator of claim 84 including a display and whereinsaid processing arrangement is configured for determining a positionalrelationship based on γ and α for presentation on said display, saidpositional relationship including the locator oriented along saidlocating direction at the above ground point and the cable in a planview. 86-91. (canceled)